# Project 6 description by domainlawyer

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```									Project VI Making and Using Childhood Growth Charts

Read through this project and work through the questions (especially the ones in boldface). Then read the designated parts of the CDC report and answer the questions in the reading guide. Use all that you have learned to prepare the What to Hand in Sheet.

1 Introduction
Most of you are probably familiar with pediatricians’ practice of plotting children’s weight and height on a growth chart. But where do these growth charts come from and what information does the pediatrician get from them? Typically a growth chart has age along the horizontal axis and either height or weight along the vertical axis, and the pediatrician will plot the child’s data on both of these. Some pediatricians instead use a single weight-to-stature chart, where stature is on the horizontal axis and weight on the vertical. Each chart usually has curves that show the 5th, 10th, 25th, 50th, 75th, 90th and 95th percentile curves. If a child’s weight lies along the 95th percentile curve on an age-to-weight chart, that means that 95 percent of other children of the same age have a lower weight. Printable examples of weight-to-age, height-to-age and weight-to-stature charts for children ages birth to 36 months or ages 2 – 20 years can be found at http://www.cdc.gov/nchs/about/major/nhanes/growthcharts/clinical_charts.htm. The CDC growth-chart homepage is http://www.cdc.gov/growthcharts . Tracking a child’s position on the growth charts is a valuable tool. A sudden change of percentiles, or consistent 5th or 95th percentile measurements can indicate a problem. Until recently, the charts that pediatricians used for children 3 years of age and older were constructed using data gathered between 1963 and 1974. The charts for children under three were constructed using data from a small sample of white middleclass children who lived near Yellow Springs, Ohio during the period 1929-1975. Once the data was gathered, fairly simple statistical techniques were used to turn the data into smooth curves like those found in the charts. Since the development of these charts, a number of concerns have been expressed about various aspects of the sampling and statistical procedures used.

Copyright 2007. Using Mathematics to Understand Our World. Developed by the Math in the Middle Institute Partnership, University of Nebraska, Lincoln. 1

To respond to these concerns, the CDC came out with new charts in 2000, using larger, more diverse, sample sizes and more advanced statistical techniques. The CDC also added a new chart to the previous ones of height-to-age, weight-to-age and weightto-stature. They added BMI-to-age. BMI stands for body-mass-index and is computed by taking weight (in kg) and dividing by height (measured in meters) squared (i.e. BMI =w/h2, but remember to use metric units). The CDC encourages pediatricians to switch to using BMI charts for several reasons • Children at different ages have different body shapes. For example, two year olds, on the whole, are a lot chubbier than four year olds. On a weight-to-height or weight-to-age charts, a tall two year old might come across as overweight, but on a BMI-to-age chart he might come out as average. • It has been discovered (using data obtained by following people from childhood into adulthood- called a longitudinal study) that childhood BMI is a slightly better indicator of future obesity in adulthood. • Since adult obesity (or lack thereof) is measured using BMI, using BMI as the measure for children allows continuity as the child progresses from teens to 20’s. In this project, we will learn more about the CDC project to produce new growth charts, how the growth charts were made, and how BMI is used to identify children at risk for obesity. We will read parts of the original CDC Report, located at www.cdc.gov/nchs/data/series/sr 11/sr11 246.pdf, we will use the data to produce our own growth chart and we will view a CDC PowerPoint presentation to learn more about BMI. There are many aspects of this project that you might be able to share with your students. If you think it would be acceptable to students and their families, we could even take BMI data from our students and compare it to the national data. Or perhaps we could find data about Nebraska students on line. During the course of the project we will discuss these possibilities. Before going on to the rest of the project, I would like to you read the first four pages of the CDC report (before getting to the first four pages, you have to scroll through about a million pages of the table of contents). Use the Reading Guide questions to help you synthesize your reading. You might also want to reference the What to Hand In sheet as you continue.

2 Constructing the Charts
In this section we will explore the methods for constructing BMI-to-age curves using the CDC data. The CDC data set is huge with literally hundreds of thousands of data points.

Copyright 2007. Using Mathematics to Understand Our World. Developed by the Math in the Middle Institute Partnership, University of Nebraska, Lincoln. 2

It takes a computer to organize that sort of data. Let’s use the CDC data and a computer program to help us generate the 75th percentile curve for BMI-to-age for girls ages 2 to 20 years. The CDC recorded data for girls ages 2, 2.5, 3, 3.5, 4, 4.5, and so on every six months until age 20, so the horizontal axis for our curve will be age marked by half years. The computer program I’ve developed (well, actually I didn’t develop it, I couldn’t develop a computer program in a million years, but I did ask someone to develop it for me) will allow you to find the 75th percentile points for each age. The program allows you to put in an age and a BMI and then it will tell you the CDC sample size for that age and the number of children who had a BMI equal to or lower than the one you put in. The URL is http://www.math.unl.edu/~nhummel2/Testing/wendy/. Get some graph paper and carefully plot the 75th percentile points. You might want to split this task amongst a group of 4 or 5 of you. It can get tedious after awhile to check every age and half age between 2 and 20. Now that you have a bunch of points, how do you turn this into a nice smooth curve that looks like the ones on the pediatrician’s charts? Can you draw a nice looking curve that fits this data pretty well? It doesn’t have to go through all the data points, it just has to be close to all the data points, and it has to be smooth without corners or points. Try it. In the 1977 charts, this is exactly how the graphs were drawn- computers plotted the data points and then a person sat down and drew a smooth curve that looked like it fit pretty well. Then mathematics was used to get a best-fit formula for this hand drawn curve (a formula was needed in order to have computers reproduce the curve or to use it in any mathematical analysis). In the new 2000 charts however, fairly advanced statistical methods were used (via computers) to draw the curves. Now compare your 75th percentile curve with the CDC’s. The CDC charts for BMI-to-age for girls 2-20, along with the original plotted points, is on pages 79 and 80 of the report. How did you do? Does the minimum of your curve occur at the same place as the minimum in the CDC curve (we’ll see soon that the location of the minimum is important).

In the CDC chart, notice that the high and low percentile curves, like the 5th and 95th for example, fit the data points less well. Why do you think that is?

Copyright 2007. Using Mathematics to Understand Our World. Developed by the Math in the Middle Institute Partnership, University of Nebraska, Lincoln. 3

The mathematics that the CDC used to generate the curves from the data is pretty sophisticated, but you can get a feel for some of it by reading parts of the report. Read the Sections: Data Exclusions, Statistical Curve Smoothing Procedures, Age and Length Groupings, Curve Smoothing Stage, and the first column of the Transformation Stage. In the Detailed Procedures by Chart section, read the subsection Length-for-Age and Stature-for-Age (it has a few sub-subsections). You won’t be able to understand most of what you read, but the Reading Guide questions will help you to identify a few of the major points. And you will get an idea as to how much mathematics (in this case statistics) can go into something as simple as creating childhood growth charts.

3 Using BMI to Indicate Risk of Adulthood Obesity
What are the chances that an overweight child will become an overweight adult? It stands to reason that overweight children are more likely to become overweight adults, but how much more likely? At what point does a child’s weight become a concern? The CDC has produced a Power Point presentation about the new 2000 charts and about using BMI in children to predict adulthood obesity. You can view the entire presentation at www.cdc.gov/nccdphp/dnpa/growthcharts/training/powerpoint or you can just view the slides that I refer you to. Along the way, I’ll include questions for you to think about. The answers to these questions will help you in preparing your answers for the questions on the What to Hand In sheet. Dr. Robert Whitaker at Children’s Hospital in Cincinnati did a longitudinal study to find out to what degree childhood BMI is related to adult obesity. To see what he found out, go to www.cdc.gov/nccdphp/dnpa/growthcharts/training/powerpoint/slides/020.htm Summarize his findings

Read about other risk factors associated with high BMI-to-age at www.cdc.gov/nccdphp/dnpa/growthcharts/training/powerpoint/slides/021.htm

Copyright 2007. Using Mathematics to Understand Our World. Developed by the Math in the Middle Institute Partnership, University of Nebraska, Lincoln. 4

Weight-to-stature charts are also good predictors of adulthood risks, but not quite as good as BMI-to-age. Look at the weight-to-stature chart for girls ages 2-20, which is included in the Charts section of this packet. Compare this to the BMI-to-age (also in the Charts section). What do you notice about the difference in the shapes of the graphs? View slides 24-27 at www.cdc.gov/nccdphp/dnpa/growthcharts/training/powerpoint/slides/024.htm www.cdc.gov/nccdphp/dnpa/growthcharts/training/powerpoint/slides/025.htm www.cdc.gov/nccdphp/dnpa/growthcharts/training/powerpoint/slides/026.htm www.cdc.gov/nccdphp/dnpa/growthcharts/training/powerpoint/slides/027.htm What is known about the relationship between adult obesity and age of adiposity rebound? If future research indicates that this is a strong link, how might that help in efforts to identify at-risk children? What are the current recommendations for overweight and at-risk categories?

You may wonder what all the fuss is about when it comes to measuring and plotting children’s BMI. Isn’t it easy to tell just by looking at a child whether or not he or she is at risk for adulthood obesity? Let’s try it! View the three slides 33, 35 and 37 (but DO NOT VIEW slides 34, 36, 38 yet) at www.cdc.gov/nccdphp/dnpa/growthcharts/training/powerpoint/slides/033.htm www.cdc.gov/nccdphp/dnpa/growthcharts/training/powerpoint/slides/035.htm www.cdc.gov/nccdphp/dnpa/growthcharts/training/powerpoint/slides/037.htm Can you guess which of these children are at risk?

The first child is a 3-year old boy whose height is 39.7 inches and weight is 41 pounds. Calculate his BMI (weight/(height)2- remember to change to metric units)

Copyright 2007. Using Mathematics to Understand Our World. Developed by the Math in the Middle Institute Partnership, University of Nebraska, Lincoln. 5

and plot it on the BMI-to-age chart for Boys age 2-20 (located at http://www.cdc.gov/nchs/about/major/nhanes/growthcharts/clinical_charts.htm). The second child is a 4-year old girl. She is 41.9 inches tall and weighs 34.5 pounds. Calculate and plot her BMI. The last child is also a 4-year old girl. She is 39.2 inches tall and weighs 38.6 pounds. Calculate and plot her BMI. Which of these children are at risk? How does the last girl compare to the first boy? What would her risk status be if she were three and not four? Why is it useful to use BMI-to-age rather than weight-to-stature?

How important is it to take precise measurements? How precise do we need to be? We’ve all had the experience of weighing five pounds more on the doctor’s scale than on our own (how does that happen anyway?). Suppose the last girl was weighed again the next day on a different scale and weighed 37.1 pounds. What would be her BMI? Her risk factor? Suppose a 5 year-old boy is 43 inches tall and 42.7 pounds. On what percentile curve is his BMI? What magnitude of error can this measurement tolerate? In particular, what sort of error in height and weight would cause him to be classified as “at risk” instead of “healthy”?

Copyright 2007. Using Mathematics to Understand Our World. Developed by the Math in the Middle Institute Partnership, University of Nebraska, Lincoln. 6

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